A device of this type is known, for example, from EP-A-0 365 621. A vertical stirring shaft with numerous aeration and/or stirring elements arranged one over the other in multiple levels is disposed in a sterilizable reactor. The aeration elements and preferably also the stirring elements are hollow in form, connected to gas feed channels and provided with at least one gas-permeable part. With its one end the stirring shaft projects through the reactor wall and is driven by an electric motor disposed outside of the reactor. Since, for example, a cell culture bioreactor must be hermetically closed, the sealing of the stirring or drive shaft rotating in the fixed reactor poses a real problem.